A266959 Smallest n-digit number ending in n.
1, 12, 103, 1004, 10005, 100006, 1000007, 10000008, 100000009, 1000000010, 10000000011, 100000000012, 1000000000013, 10000000000014, 100000000000015, 1000000000000016, 10000000000000017, 100000000000000018, 1000000000000000019, 10000000000000000020
Offset: 1
Examples
a(4) = 1004 because it is the smallest 4-digit number ending in 4.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (12,-21,10).
Programs
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Magma
[1] cat [n+10^(n-1): n in [2..30]]; // Vincenzo Librandi, Jan 10 2016
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Maple
A266959:=n->n+10^(n-1): 1, seq(A266959(n), n=2..30);
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Mathematica
Join[{1}, Table[n + 10^(n - 1), {n, 2, 20}]] -
PARI
Vec(x*(1-20*x^2+10*x^3)/((1-x)^2*(1-10*x)) + O(x^30)) \\ Colin Barker, Jan 10 2016
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PARI
a(n) = if(n==1, 1, n + 10^(n-1)); \\ Altug Alkan, Jan 17 2016
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Python
def A266959(n): return n+10**(n-1) if n > 1 else 1 # Chai Wah Wu, Jul 25 2022
Formula
a(n) = n + 10^(n-1) for n>1 with a(1) = 1.
a(n) = A081552(n) - 1 for n>1. - Michel Marcus, Jan 10 2016
From Colin Barker, Jan 10 2016: (Start)
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n>3.
G.f.: x*(1-20*x^2+10*x^3) / ((1-x)^2*(1-10*x)). (End)
Comments